Optical coherence tomography (OCT) is a noninvasive, noncontact imaging modality that uses coherence gating to obtain high-resolution cross-sectional images of tissue microstructure. Several implementations of OCT have been developed. In frequency domain OCT (FD-OCT), the interferometric signal between light from a reference and the back-scattered light from a sample point is recorded in the frequency domain typically either by using a dispersive spectrometer in the detection arm in the case of spectral-domain OCT (SD-OCT) or rapidly tuning a swept laser source in the case of swept-source OCT (SS-OCT). After a wavelength calibration, a one-dimensional Fourier transform is taken to obtain the scattering profile of a sample along the OCT beam. Each scattering profile is called an axial scan, or A-scan. Cross-sectional images, called B-scans, and by extension 3D volumes, are built up from many A-scans, with the OCT beam illuminating a set of transverse locations on the sample either by scanning or field illumination.
Functional OCT can provide important clinical information that is not available in the typical intensity based structural OCT images. There have been several functional contrast enhancement methods including Doppler OCT, Phase-sensitive OCT, Polarization Sensitive OCT, Spectroscopic OCT, etc. Integration of functional extensions can greatly enhance the capabilities of OCT for a range of applications in medicine.
One of the most promising functional extensions of OCT has been the field of OCT angiography which is based on flow or motion contrast between repeated structural OCT measurements. A variety of OCT Angiography techniques have been developed including but not limited to optical microangiography (OMAG), speckle variance, phase variance, correlation mapping, and decorrelation (see for example US Patent Publication No. 2008/0025570, US Patent Publication No. 2010/0027857, US Patent Publication No. 2012/0307014, Fingler et al. “Mobility and transverse flow visualization using phase variance contrast with spectral domain optical coherence tomography” Opt. Express 2007; 15:12636-53, Mariampillai et al., “Speckle variance detection of microvasculature using swept-source optical coherence tomography”, Optics Letters 33(13), 1530-1533, 2008, An et al., “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438-11452, 2008, Enfield et al., “In vivo imaging of the microcirculation of the volar forearm using correlation mapping optical coherence tomography” (cmOCT), Biomed. Opt. Express2(5), 1184-1193, 2011, and Jia et al. “Split-spectrum amplitude decorrelation angiography with optical coherence tomography” Optics Express 20(4) 4710-4725 (2012), the contents of all of which are hereby incorporated by reference). These techniques use the OCT data to achieve the imaging of functional vascular networks within microcirculatory tissue beds in vivo, without the use of exogenous contrast agents.
The key point of OCT angiography processing methods is to extract localized signal variations from the bulk motion signal of a background tissue by comparing OCT signals, such as B-scans, captured at different closely-spaced time points (inter-frame change analysis). Processing can be carried out on the complex OCT data (complex-based), the amplitude or intensity portion of the OCT data (intensity-based), or the phase portion of the data (phase-based). The separately processed intensity and phase information can also be combined in some approaches. One of the major applications of flow contrast techniques (e.g., intensity-based, phase-based, complex-based, etc.) has been to generate en face vasculature images of the retina (angiogram). High resolution en face visualization based on inter-frame change analysis requires high density of sampling points and hence the time required to finish such scans can be up to an order of magnitude higher compared to regular cube scans used in commercial OCT systems.
While OCT angiography appears to be an exciting technology, there are several technical limitations that need to be overcome before it can gain widespread acceptance in clinical settings. One of the major limitations of OCT angiography is the long acquisition times and associated motion artifacts that can affect analysis. US Patent Publication No. 2013/0176532 and International Application No. PCT/EP2016/072493, both of which are hereby incorporated by reference, describe some methods for dealing with motion artifacts in OCT Angiography data.
Another limitation with OCT angiography technology is the occurrence of projection or decorrelation tail artifacts in the OCT angiography images. Light passing through a blood vessel can be reflected, refracted, or absorbed. The light reflected from blood moving in the vessels forms the basis of optical coherence tomography angiography (OCTA). However, the light that has passed through moving blood also encounters tissue below the blood vessel. When this light strikes the deeper layers in the eye, such as the retinal pigment epithelium (RPE) layer of retina, it is reflected back to the OCT instrument. The light that has passed through the blood vessels changes over time, and so the reflected portion of this light is detected as having a decorrelation resembling blood flow. Therefore, the RPE will seem to have blood vessels that have the pattern of the overlying retinal blood vessels. This effect is referred to as the OCTA projection artifact. OCTA projection artifacts also occur from superficial retinal vessels, which can be seen in deeper retinal layers, or retinal and choroidal vessels which can be even seen deep in the sclera. OCTA projection artifacts are nearly always present and seen in any structure that is located below vasculature.
Previous methods that are used to reduce the projection artifacts include:                1) Subtracting an angiogram generated based on deeper layers from the angiogram generated from the superficial layers directly after some preprocessing steps. In this method, a true angiographic image for the subretinal space can be obtained by a simple subtraction of a scaled image obtained from the retinal space from the image obtained from the subretinal space (see for example, Zhang, Anqi, Qinqin Zhang, and Ruikang K. Wang. “Minimizing projection artifacts for accurate presentation of choroidal neovascularization in OCT micro-angiography.” Biomedical Optics Express 6.10 (2015): 4130-4143.).        2) Removing flow projection artifacts from superficial retinal blood vessels to the outer retina by first generating a binary large inner retinal vessel map based on applying a 30×30 pixel Gaussian filter. This filter removed small inner retinal vessels and masked the outer retina flow map, thus enabling the subtraction of large vessel projections. A binary outer retinal flow map was then generated by applying a 10×10 pixel Gaussian filter to remove remaining noise and mask the outer retinal flow map again to obtain a clear map. After these artifacts are removed by the mask subtraction operation, there were no longer any flow artifacts in the normally avascular outer retina (see for example, Jia, Yali, et al. “Quantitative optical coherence tomography angiography of choroidal neovascularization in age-related macular degeneration.”Ophthalmology 121.7 (2014): 1435-1444).        
Here we describe a new mathematically sound approach for removing the flow projection artifacts based on an inverse problem estimation framework.